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Warm Up/ Activator. Using scissors and a ruler, cut out a triangle from a piece of colored paper. Clean up your area afterwards. We will be using the triangle during our lesson today. . Constructing Triangles. Common Core 7.G.2. Vocabulary. Uniquely defined Ambiguously defined Nonexistent.

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warm up activator

Warm Up/ Activator

Using scissors and a ruler, cut out a triangle from a piece of colored paper. Clean up your area afterwards. We will be using the triangle during our lesson today.

constructing triangles

Constructing Triangles

Common Core 7.G.2

vocabulary
Vocabulary
  • Uniquely defined
  • Ambiguously defined
  • Nonexistent
triangle inequality theorem
Triangle Inequality Theorem

Let’s review what we learned yesterday with this video.

http://www.youtube.com/watch?v=OoLb_NnnKSQ

triangle inequality theorem1
Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

z

x

y

practice
Practice

Can these measures be the sides of a triangle?

  • 7, 5, 4
  • 2, 1, 5
  • 9, 6, 3
  • 7, 8, 4
practice1
Practice

Can these measures be the sides of a triangle?

  • 7, 5, 4 yes
  • 2, 1, 5 no
  • 9, 6, 3 no
  • 7, 8, 4 yes
example 1
Example 1

Using the measurements 6 in and 8 in, what is the smallest possible length of the third side? What is the largest possible length of the third side?

example 11
Example 1

If you assume that 6 and 8 are the shorter sides, then their sum is greater than the third side. Therefore, the third side has to be less than 14.

example 12
Example 1

If you assume that the larger of these values, 8, is the largest side of the triangle, then 6 plus the missing value must be greater than 8. Therefore, the third side has to be more than 2.

example 13
Example 1

If you put these two inequalities together, then you get the range of values that can be the length of the third side:

Therefore, any value between 2 and 14 (but not equal to 2 or 14) can be the length of the third side.

practice2
Practice

Solve for the range of values that could be the length of the third side for triangles with these 2 sides:

  • 2 and 6
  • 9 and 11
  • 10 and 18

(Be sure to look for patterns!)

practice3
Practice

Solve for the range of values that could be the length of the third side for triangles with these 2 sides:

  • 2 and 6
  • 9 and 11
  • 10 and 18

What patterns do you see?

types of triangles
Types of Triangles

If three side lengths do not make a triangle, you would say that the triangle is nonexistent.

If three side lengths do make a triangle, you would say that the triangle is uniquely defined because it creates one, specific triangle.

angles of triangles
Angles of Triangles

Tear off the corners of the triangle that you created in the warm up/activator. Lay them on your paper with all of the vertices pointing inwards and the edges touching. Like this:

What do they create?

angles of triangles1
Angles of Triangles

What do they create? A straight line, which is equal to 180 degrees; therefore, the sum of the angles in a triangle always equal 180 degrees. This is called the Triangle Angle Sum Theorem. Glue your triangle corners in your math notebook and explain this in your own words.

practice4
Practice

Given the following angle measurements, determine the third angle measurement.

Do these measurements create triangles?

3.

4.

practice5
Practice

Given the following angle measurements, determine the third angle measurement.

Do these measurements create triangles?

3. yes

4. no

constructing triangles from angles
Constructing Triangles from Angles

Look at these triangles. They have the same angle measurements, which is why they are similar in shape. However, do they have the same side lengths?

constructing triangles from angles1
Constructing Triangles from Angles

Look at these triangles. They have the same angle measurements, which is why they are similar in shape. However, do they have the same side lengths? No.

Since they aren’t the same size, will angle measurements construct unique triangles?

constructing triangles from angles2
Constructing Triangles from Angles

Look at these triangles. They have the same angle measurements, which is why they are similar in shape. However, do they have the same side lengths? No.

Since they aren’t the same size, will angle measurements construct unique triangles? No.

constructing triangles from angles3
Constructing Triangles from Angles

Conditions, such as angle measurements, that can create more than one triangle are called ambiguously defined.

summary
Summary

Take turns with your partner explaining the Triangle Angle Sum Theorem and the Triangle Inequality Theorem in your own words.